Problem: Rewrite as a simplified fraction. ${2.7\overline{96} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2796.9696...\\ 10x &= 27.9696...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2769}$ ${x = \dfrac{2769}{990}} $ ${x = \dfrac{923}{330}} \text{or} {2 \dfrac{263}{330}}$